ApCoCoA-1:LinSyz.BettyNumber

LinSyz.BettyNumber

Computes the N-th Betty number of a module generated by linear forms.

Syntax

LinSyz.BettyNumber(M:MODULE,N:INT):INT

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

This command computes the N-th Betty number of a given module which is generated by vectors consisting of linear forms. Be aware of the fact that this is not well tested and may contain bugs! Also the linear forms may not have any constant component, so if your system has some, you have to homogenize the system first via introducing a new indeterminate.

• @param M A module for which the N-th Betty number is computed.

• @param N Declares which Betty number will be computed.

Example

Use P::=QQ[x,y,z];
M:=Module([[x+y+z,x+y+z,x-y+z],[x-y,y-4z,x+2z],[x,y,z]]);
BettiDiagram(M);
        0
----------
 1:     3
----------
Tot:    3
-------------------------------
LinSyz.BettyNumber(M,0);
ERROR: BettyNumber: Second parameter must be positive!
CONTEXT: Error(<quotes>BettyNumber: Second parameter must be positive!</quotes>)
-------------------------------
LinSyz.BettyNumber(M,1);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
3
-------------------------------
LinSyz.BettyNumber(M,2);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
0
-------------------------------
LinSyz.BettyNumber(M,3);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
0
-------------------------------

See also

LinSyz.BettyNumbers

LinSyz.Resolution

LinSyz.SyzModule

Introduction to Modules